import matplotlib.pyplot as plt
import numpy as np

a = np.linspace(0, 1, 1000)

# 修正后的参数方程（注意变量η的完整应用）
sample_x = (8 + np.sin(4 * np.pi * a)) * np.cos(np.pi * 2 * a) + 4
sample_y = (8 + np.cos(4 * np.pi * a)) * np.sin(2 * np.pi * a) + 4

# 绘制曲线
plt.figure(figsize=(8, 8))

plt.plot(sample_x, sample_y, "b-", label="Curve")

# 添加采样点标记（红色圆圈+星号边框）
# plt.scatter(sample_x,sample_y,
#             marker='o',           # 圆形标记
#             c='red',              # 填充颜色
#             linewidths=2,         # 边框粗细
#             label='Samples')

plt.axis("equal")
plt.legend()
plt.show()
